From how I understand your blurb, what you're getting at is the increasing orthodoxy of Christianity in Europe, following the conversion process.

As regards England, conversion began in the late sixth century with Augustine's mission to Kent. Whether the clergy today doesn't like the idea of pagan syncretism I can't say, but they certainly did in the Early Middle Ages. Pope Gregory the Great, who sent Augustine and later Mellitus (who was to become Bishop of London) said the following in a letter during Mellitus's journey to England: "tell [Augustine] what I have decided after long deliberation concerning the affair of the English:... the temples of the idols in that nation ought not to be destroyed; but let the idols, which are in them, be destroyed; let water be blessed and sprinkled in the said temples, altars erected and relics placed there. For, if those temples are well built, it is needful that they should be converted from the worship of devils to the service of the true God; that the nation... may the more familiarly resort to the places to which they have been accustomed. And because they are accustomed to slaughter many oxen in sacrifice to devils, some solemnity ought to be given to them in exchange for this also; as that, on the day of dedication, or the nativities of the holy martyrs... no longer sacrifice animals to the devil, but kill cattle for their food and to the praise of God... that, while some outward rejoicings are preserved for them, they may be able the more easily to consent to the inward joys. For there is no doubt that it is impossible to cut off everything at once from their obdurate hearts, for he who strives to ascend to the highest place, rises by degrees or steps, not by leaps."

The last phrase - "he who strives to ascend to the highest places, rises by degrees or steps, not by leaps" - epitomises Gregory's approach, and the early English Church. Efforts were made so that, perhaps not the most orthodox Christianity, but Christianity nonetheless, took hold in England. In the decades following Augustine's 597 landfall in Kent, Christianity remained a minority and tenuous religion. Æthelberht, the first Christian king, passed the throne of Kent to pagans on his death. For others like Rædwald of East Anglia, the dual worship of both pagan gods and Jesus Christ was a sort of double insurance against misfortune. Beyond that, in a large part it seems that Christianity was a political move over a spiritual one. Kent, and the south and especially east of England more generally, had long associations with the Continent. Æthelberht's wife Bertha was a Frank, for example. As Christianity became further embedded in Merovingian France, it was to the advantage of English rulers to follow suite. So, while increasing parts of England were at least nominally Christian for much of the seventh century, this had little bearing on how widespread Christianity was - to say nothing of its accordance with Roman Christianity.

Beginning in the 670s, though, Christianity moved beyond a politically advantageous choice. It was in this period of about 670 to the 740s that a monastic boom took place in England, with the foundation of numerous Christian institutions across the island. Bede famously decried many as corrupt, for "others by a still heavier crime, since they are laymen and not experienced in the usages of the life according to the rule or possessed by love of it, give money to kings, and under the pretext of founding monasteries buy lands on which they may more freely devote themselves to lust, and in addition cause them to be ascribed to them in hereditary right by royal edicts." To trust Bede would seem to say that once again Christianity was really nothing more than an opportunity for personal gain - in this case of inheritable land rights. However, I side here with the ideas of P Sims-Williams, who has argued that Bede was employing nothing more than a standard monastic polemic technique. What seems to really be happening, is the foundation of religious institutions within households. This was a fairly common practice in the Mediterranean world, and what Bede's argument really boiled down to was griping over a strict or loose interpretation of monastic obligation. These household, or family monasteries, then, shouldn't be discounted as non- or nominally Christian, but rather just not as militantly so (Bede goes on to say that the people of these monasteries were simply household members, presumably as opposed to being raised in a monastic foundation as oblates like himself). The christianity of these institutions seems all the more tenable for me when taken in wider context. It was during the eighth century (Bede wrote his letter in 734) that the Anglo-Saxon Chronicle describes a string of kings abdicating for a life of monasticism, or traveling to Rome to die. To surrender power of a kingdom to pursue a religious goal hardly seems the actions of the politically greedy, but rather the pious and devout. It is telling too that during this period the pressing issues at hand were no longer whether or not to be Christian, but rather questions of faith itself.

As the centuries pass, the English church continued to develop and further align itself with Continental notions. Offa's move in the eighth century to establish an archbishopric in Lichfield, while on the one hand politically driven (allowing Offa to consecrate a successor), shows too an attempt to work within a Continental mindset. Not long earlier, Charlemagne, who was in contact with Offa, had consecrated heirs. Were Offa to have succeeded in choosing a lasting heir, that Christian-based process would be the first of its kind in England, as opposed to the norm of interregnum wars for the throne. Furthermore, Offa's attempt can be looked at alongside Gregory the Great's initial goal of twenty-four sees and two metropolitans in England, a goal as yet incomplete. Later on in the 10th century, the Benedictine reforms emanating from Cluny and Fleury abbeys took hold in England, spurring the adoption of a formal monastic rule in England. The argument, like Bede 200 years prior, fell along the lines of strict and loose clergy, and ultimately was resolved in alignment with Cluniac ideas.

A transition, from variegated, syncretic Christianity to increasingly orthodox and Rome-centric Christianity is not isolated to England. Farther north, Iceland formally converted in 1000 AD. In a large part, though, early bishops in Iceland were essentially the same as chiefs, and non-celibacy and simony were not uncommon. Accordingly during the Hildebrandine reforms of the late eleventh century (works by Pope Gregory VII against simony and lay investiture), Iceland remained unaffected (albeit by willful ignorance or not I'm not so sure) for decades.

To paint in broad brushstrokes, then, Christianity in Europe can be broken down into two phases as it spread: one of nominal conversion, and the long following period of alignment with Rome. As I understand it, this alignment is what you're getting at with the idea of being "'religionized.'" Granted, this answer was speaking pretty loosely and in terms mostly of England, but I think you'll find similar situations play themselves out in Scandinavia, Germany, and elsewhere where the Christianity of the Roman Empire needed re-establishing (or establishing in the first place).

Sources:

For Gregory's letter my translation of Bede was English Historical Documents volume I no. 151, likewise Ecgbert's letter for Bede's opinion on family monasteries is EHD no. 170

Anglo Saxon Chronicle: http://avalon.law.yale.edu/subject_menus/angsax.asp

For family monasteries and Bede's polemic, P Sims-Williams, Religion and Literature in Western England, 600-800

For Iceland, William Ian Miller, Bloodtaking and Peacemaking: Feud, Law, and Society in Saga Iceland